A model for the Kolbe reaction of acetate in a parallel-plate reactor

A mathematical model is developed for the study of the Kolbe oxidative dimerization of acetate to ethane and carbon dioxide in a parallel-plate reactor operating at a fixed cell potential, with hydrogen evolution being the cathode reaction. The volume of gas evolved into the interelectrode gap is tracked by constructing a hypothetical gas layer which increases in thickness with the streamwise direction in a manner determined by solution to the model equations; concurrently, the liquid flows in a hypothetical layer which decreases in thickness. The three-component gas phase is assumed to be ideal, and the liquid phase is an aqueous mixture of five species: acetate, proton, sodium and hydroxyl ions and acetic acid. The model predicts the concentration profiles and the streamwise variation of the gas-void fraction, reaction current density and liquid and gas velocities. Gas evolution causes a decreasing current density in the streamwise direction and an increasing gas and liquid velocity. The concentrations of acetic acid and proton decrease in the streamwise direction, while hydroxyl concentration increases; the decrease in acetate concentration, however, is not significant until the local base-to-acid ratio is near unity because of the buffering effect from undissociated acetic acid. The average current density increases with inlet solution velocity and cell potential and asymptotically approaches the secondary current limit. There exists an optimal interelectrode separation where the cell resistance is minimum. The average current density exhibits a shallow maximum with the baseto-acid ratio of the feed, but decreases precipitously when the ratio is near unity due to the rapid decrease in the proton concentration.Nomenclature b _a anodic Tafel constant of the Kolbe reaction of acetate (V) - b _c cathodic Tafel constant of hydrogen evolution reaction (V) - c ₁ acetate concentration, mol cm^–3 - c ₁, ref reference concentration of acetate (mol cm^–3) - c ₂ acetic acid concentration (mol cm^–3) - c ₃ proton concentration (mol cm^–3) - c ₃, ref reference concentration of proton (mol cm^–3) - c ₄ hydroxyl concentration (mol cm^–3) - C _A stoichiometric concentration of acetic acid in the feed stream (mol cm^–3) - C _B stoichiometric concentration of sodium hydroxide in the feed stream (mol cm^–3) - c _B/A C _B/C _A, base-to-acid ratio in the feed stream (sodium hydroxide to acetic acid) - c _i(0) concentration of species i at cell inlet (mol cm^–3) - c _i ^* c _i/c _A - E _d decomposition potential (V) - E _neq,a ^o standard open-circuit potential of the Kolbe reaction of acetate (V) - E _eq,a ^o open-circuit potential of the Kolbe reaction of acetate (V) - E _eq ^c standard open-circuit potential of hydrogen evolution reaction (V) - E _eq,e open-circuit potential of hydrogen evolution reaction (V) - F Faraday constant (96 487 C equiv.^–1) - f gas-void fraction - h cell height (cm) - IR ohmic-voltage drop in the electrolyte (V) - i current density (A cm^–2) - i _a,ref exchange current density of acetate Kolbe reaction at reference concentration (A cm^–2) - i _c,ref exchange current density of hydrogen evolution reaction at a reference concentration (A cm^–2) - i _avg average current density (A cm^–2) - i(0) current density at the inlet of the cell (A cm^–2) - i ^* i/i(00) - Ka ionization constant of acetic acid (mol cm^–3) - K _a ^* K _a/c _A     

Ozone generation via the electrolysis of fluoboric acid using glassy carbon anodes and air depolarized cathodes

An electrochemical ozone generation process was studied wherein glassy carbon anodes and air depolarized cathodes were used to produce ozone at concentrations much higher than those obtainable by conventional oxygen-fed corona discharge generators. A mathematical model of the build up of ozone concentration with time is presented and compared to experimental data. Products based on this technology show promise of decreased initial costs compared with corona discharge ozone generation; however, energy consumption per kg ozone is greater. Recent developments in the literature are reviewed.Nomenclature A electrode area (m²) - Ar ^* modified Archimedes number, d _b ³ g_G/² (1 — _G) - C _{O 3 (aq)} concentration of dissolved ozone (mol m^–3) - C _{O 3 i} concentration at interface (mol m^–3) - C _{O 3 1} concentration in bulk liquid (mol m^–3) - D diffusion coefficient (m² s^–1) - E electrode potential against reference (V) - F charge of one mole of electrons (96 485 C mol^–1) - g gravitational acceleration (9.806 65 m s^–2) - i current density (A m^–2) - i ₁ limiting current density (A m^–2) - I current (A) - j material flux per unit area (mol m^–2 s^–1) - k _obs observed rate constant (mol^–1 s^–1) - k _t thermal conductivity (J s^–1 K^–1) - L reactor/anode height (m) - N _{O 3} average rate of mass transfer (mol m^–2 s^–1) - Q heat flux (J s^–1) - r _i radius of anode interior (m) - r _a radius of anode exterior (m) - r _c radius of cathode (m) - R gas constant (8.314 J K^–1 mol^–1) - S _c Schmidt number, v/D - Sh Sherwood number, k _m d _b/D = i _L d _b/zFD[O₃] - t time (s) - T _i temperature of inner surface (K) - T _o temperature of outer surface (K) - U reactor terminal voltage (V) - electrolyte linear velocity (m s^–1) - V volume (m³) - V _{O 3} volume of ozone evolved (10^–6 m³ h^–1) - z _i number of Faradays per mole of reactant in the electrochemical reaction Greek symbols _G gas phase fraction in the electrolyte - (mean) Nernst diffusion layer thickness (m) - fractional current efficiency - overpotential (V) - electrolyte kinematic viscosity (m² s^–1) - electrolyte resistivity (V A^–1 m)     

Modelling of time-dependent performance criteria in a three-dimensional cell system during batch recirculation copper recovery

A three-dimensional electrode cell with cross-flow of current and electrolyte is modelled for galvanostatic and pseudopotentiostatic operation. The model is based on the electrodeposition of copper from acidified copper sulphate solution onto copper particles, with an initial concentration ensuring a diffusion-controlled process and operating in a batch recycle mode. Plug flow through the cell and perfect mixing of the electrolyte in the reservoir are assumed. Based on the model, the behaviour of reacting ion concentration, current efficiency, cell voltage, specific energy consumption and process time on selected independent variables is analysed for both galvanostatic and pseudopotentiostatic modes of operation. From the results presented it is possible to identify the optimal values of parameters for copper electrowinning.List of symbols a specific surface area (m^–1) - A cross-sectional area (mu²) - a _a Tafel constant for anode overpotential (V) - a _II Tofel constant for hydrogen evolution overpotential (V) - b _a Tafel coefficient for anode overpotential (V decade^–1) - b _H Tafel coefficient for hydrogen evolution overpotential (V decade^–1) - C _e concentration at the electrode surface (m) - C _L cell outlet concentration (m) - C ₀ cell inlet concentration (m) - C ₀ ⁰ initial cell inlet concentration att = 0 (m) - d _p particle diameter (m) - e, e _p current efficiency and pump efficiency, respectively - E specific energy consumption (Wh mol^–1) - E solution phase potential drop through the cathode (V) - F Faraday number (C mol^–1) - h interelectrode distance (m) - i, i _L current density and limiting current density, respectively (A m^–2) - I, I _L current and limiting current, respectively (A) - I _H partial current for hydrogen evolution (A) - k _L mass transfer coefficient (m s^–1) - L bed height (m) - l bed depth (m) - M molecular weight (g mol^–1) - N power per unit of electrode area (W m^–2) - n exponent in Equation 19 - P pressure drop in the cell (N m^–2) - Q electrolyte flow rate (m³ h^–1) - R Universal gas constant (J mol^–1 K^–1) - r _e electrochemical reaction rate (mol m^–2 h^–1) - t _c critical time for operating current to reach instantaneous limiting current (s) - t _p process time to reach specified degree of conversion (s) - T temperature (K) - u electrolyte velocity (m s^–1) - U total cell voltage (V) - U ₀ reversible decomposition potential (V) - U _ohm ohmic voltage drop between anode and threedimensional cathode (V) - V volume of electrolyte (m³) - z number of transferred electrons Greek letters ratio of the operating and limiting currents - _{A, a} anodic activation overpotential (V) - _{c, e} cathodic concentration overpotential (V) - bed voidage - _H void fraction of hydrogen bubbles in cathode - constant (Equation 2) - ₀ electrolyte conductivity (ohm^–1 m^–1) - v electrolyte kinematic viscosity (m² s^–1) - _d diaphragm voltage drop (V) - _H voltage drop due to hydrogen bubble containing electrolyte in cathode (V) - electrolyte density (kg m^–3) - _p particle density (kg M^–3) - reservoir residence time (s)     

Computer simulation of high-discharge-rate battery systems

Simulations were carried out for a proposed two-dimensional high-discharge-rate cell under load with an interelectrode gap of the order of 100 m. A finite difference program was written to solve the set of coupled, partial differential equations governing the behaviour of this system. Cell dimensions, cell loads, and kinetic parameters were varied to study the effects on voltage, current and specific energy. Trends in cell performance are noted, and suggestions are made for development of cells to meet specific design criteria. Modelling difficulties are discussed and suggestions are made for improvement.Nomenclature A surface area of unit cell (cm²) - A _k conductivity parameter (cm^{2 –1} mol^–1) - b Tafel slope (V) - c concentration (mol cm^–3) - c ₀ concentration of bulk electrolyte (mol cm^–3) - D diffusivity (cm² s^–1) - D _h lumped diffusion parameter (J s cm^–2 mol^–1) - D _s lumped diffusion coefficient (A cm² mol^–1) - E rest potential of electrode (V) - F Faraday constant (96 500 C mol^–1) - i current density (A cm^–2) - I total current for unit cell (A) - i ₀ exchange current density (A cm^–2) - N flux of charged species (mol cm² s^–1) - R gas constant (8.314 J mol^–1 K^–1) - R _ext resistance external to cell () - t time (s) - T temperature (K) - t ₀ transference number - u mobility (cm² mol J^–1 s^–1) - V volume of an element in the cell (cm³) - V _ext voltage external to cell (V) - z charge on an ion - _c concentration overpotential (V) - _s surface overpotential (V) - conductivity (^–1 cm^–1) - stoichiometric coefficient - electric potential in solution (V)     

Determination of overall mass transport coefficients in gas diffusion electrodes

Gas diffusion electrodes are used for many purposes, for example in fuel cells, in synthesis and as anodes in electrodeposition processes. The behaviour of gas diffusion electrodes has been the subject of many studies. In this work the transport of gas in the gas diffusion electrode, characterized by the overall mass transport coefficient, has been investigated using hydrogen-nitrogen mixtures. A reactor model for the gas compartment of the gas diffusion electrode test cell is proposed to calculate the concentration of hydrogen in the gas compartment as a function of the input concentration of hydrogen and the total volumetric gas flow rate. The mass transport coefficient is found to be independent of variations in hydrogen concentration and volumetric gas flow rate. The temperature dependence of the mass transport coefficient has been determined. A maximum was found at 40°C.Notation Agd geometric electrode surface area (m²) - C _in concentration of reactive component at the inlet of the gas compartment (mol m^–3) - c _out concentration of reactive component at the outlet of the gas compartment (mol m^–3) - E potential (V) - E _e equilibrium potential (V) - E _t upper limit potential (V) - F _v volumetric flow rate (m^–3 s^–1) - F _v,H volumetric flow rate of hydrogen (m^–3 s^–1) - F _v,N volumetric flow rate of nitrogen (m^–3 s^–1) - F _vin volumetric flow rate at the inlet of the gas compartment (m^–3 s^–1) - F _v,out volumetric flow rate at the outlet of the gas compartment (in ^–3 s^–1) - F _v,reaction volumetric flow rate of reactive component into the gas diffusion electrode (m^–3 s^–1) - Faraday constant (A s mo^–1) - I _gd current for gas diffusion electrode (A) - i _gd current density for gas diffusion electrode (A m^–2) - I _gd,1 diffusion limited current for gas diffusion electrode (A) - i _gd,1 diffusion limited current density for gas diffusion electrode (A m^–2) - I _gd,1,calc calculated diffusion limited current for gas diffusion electrode (A) - i _gd,1,calc calculated diffusion limited current density for gas diffusion electrode (A m^–2) - I _hp current for hydrogen production (A) - k _s mass transport coefficient calculated from c _out (m s^–1) - n number of electrons involved in electrode reaction - T temperature (°C) - V _m molar volume of gas (m³ mol^–1) - overpotential (V)     

The effect of the type of electric current on the cathodic corrosion of aluminium

A comparative experimental study on the cathodic corrosion of aluminium in 0.52 M sodium chloride distilled water solutions is carried out. The electrolysis is conducted using a single half-cycle rectified, direct or industrial frequency current. Characteristic relationships concerning the cathodic corrosion are noted. Attention is drawn to the higher rates of cathodic corrosion observed on electrolysis with single half-cycle rectified current which is combined with lower energy costs.Nomenclature w _k1 cathodic corrosion rate for direct current electrolysis (g s^–1 m^–2) - w_k2 cathodic corrosion rate for single half-cycle rectified current electrolysis (g s^–1 m^–2) - w _a anodic dissolution rate (g s^–1 m^–2) - w _F theoretical Faradaic dissolution rate (g s^–1 m^–2) - w dissolution rate for alternating current electrolysis (g s^–1 m^–2) - j electric current density (A m^–2)     

A study of transport of hydroxyl ion in a chlor-alkali diaphragm

The loss of hydroxyl ions by diffusion and back migration to the anolyte compartment is the major source of efficiency loss in a chlor-alkali diaphragm cell. The transfer rate of hydroxyl ions across the diaphragm depends on diaphragm properties and electrolyte flow rate inside the diaphragm. This work examines the concentration distribution of hydroxyl ions across the diaphragm in a laboratory cell. A numerical computation is carried out to optimize the diaphragm structure and current density based on the minimum production cost of chlorine. The optimum current density is found to be 50% lower than the present operating current density in the chlor-alkali industry.Nomenclature A _p apparent cross-sectional area of the diaphragm (m²) - A _T true cross-sectional area of the pores (m²) - C _OH concentration of the hydroxyl ion at any pointx along thex-direction (kg mol m^–3) - C _K catholyte concentration (kg mol m^–3) - C dimensionless concentration given in Equation 11 - C _D unit diaphragm cost ($ kg^–1) - C _E unit direct electrical energy cost ($ kg^–1) - C ₁ unit specific investment cost ($ kg^–1) - D diffusion coefficient of the hydroxyl ion (m² s^–1) - E ₀ open circuit voltage (V) - E total cell voltage (V) - F Faraday's constants (96 487 C g equiv^–1) - i _P apparent current density based on apparent area of the diaphragm,A _P (A m^–2) - i _T true current density based on true crosssectional area of the pores,A _T (A m^–2) - I magnitude of total current through the cell (A) - (IR)_BUS voltage drop in the bus-bar (V) - (IR)_SOLN voltage drop in the solution (V) - (IR)_DIA voltage drop in the diaphragm (V) - N _OH flux of hydroxyl ion (kg mol m^–2 s^–1) - K _S average conductivity of the solution (ohm^–1 m^–1) - k ₁ energy cost ($ kWh^–1) - K ₂ capital cost of the electrolyte cell ($ m^–2) - K ₃ cost coefficient of diaphragm ($ m^–2) - K ₅ unit cost of the raw material ($ kg^–1) - l effective pore length (m) - l ₁ distance between the anode and the cathode (m) - L life period of the diaphragm (yr) - molecular weight of chlorine gas (kg) - M _NaCl molecular weight of sodium chloride (kg) - n number of years of amortization which in principle is given by the life time of the cell (yr) - N _C total number of cells (dimensionless) - p production rate of chlorine gas (kg yr^–1) - R resistance (ohm) - r ₀ resistance of the solution (ohm) - S annual interest rate (%) - U _OH– mobility of hydroxyl ion (kg mol m²V^–1 C^–1 s^–1) - electrolyte velocity along the x-direction inside diaphragm (m s^–1) - _S superficial velocity (m s^–1) - V _W volume of water lost from the catholyte compartment due to evaporation and cathodic reaction (m³ s^–1) - x axial coordinate - Z valence of hydroxyl ion (kg equiv kg^–1 mol^–1) - diaphragm thickness (m) - porosity (%) - current efficiency (dimensionless) - _a anodic overpotential (V) - _c cathodic overpotential (V) - tortuosity factor (dimensionless)     

On the relative Coulombic effectiveness and profitability of electrolysis via intermittent current

The current and energy utilization of intermittent current electrolysis is analysed, and feasibility regions in terms of product costs and profitability are discussed using the deposition of copper as an illustrative example.Nomenclature A electrode area - b geometric aspect ratio,W/L - c ₀ bulk electrolyte concentration - C _E Unit price or electricity, including generation of intermittent potential-drop train (MU J^–1) - C _p unit price of electrolysis product (MU kg^–1) - D electrolyte diffusivity - E relative Coulombic effectiveness - F Faraday's constant - h chart recording heights (Fig. 1) - I current - I _m maximum allowable current in d.c. electrolysis - k mass transfer coefficient - L length of straight section in current response (Fig. 1) - MU arbitrary monetary unit - m _e electrochemical coefficient of product (kg C^–1) - n number of electrons involved in cathode reaction - N number of cycles in intermittent potential train - P unit profit (MU kg^–1) - r chart recording height ratio, or corresponding current ratioh ₁/h ₂=I ₁/I ₂ - S _I root mean square of deviations about the fitted curve - t time - V _c magnitude of intermittent potential drop (V) - V _m maximum allowable potential drop in d.c. electrolysis (V) - W length of trapezoidal portion in response (c) (Fig. 1) - X potential drop ratioV _c/V _m - Y ratio of unit profits - Z _i functions defined in Equation 9b (Z₁) and Equation 10b (Z₂) - lumped parameter (Equation 4) - chart response angle - half-period of intermittent potential-drop Train     

Applications of magnetoelectrolysis

A broad overview of research on the effects of imposed magnetic fields on electrolytic processes is given. As well as modelling of mass transfer in magnetoelectrolytic cells, the effect of magnetic fields on reaction kinetics is discussed. Interactions of an imposed magnetic field with cathodic crystallization and anodic dissolution behaviour of metals are also treated. These topics are described from a practical point of view.Nomenclature 1, 2 regression parameters (-) - B magnetic field flux density vector (T) - c concentration (mol m^–3) - c bulk concentration (mol m^–3) - D diffusion coefficient (m² s^–1) - d _e diameter of rotating disc electrode (m) - E electric field strength vector (V m^–1) - E _i induced electric field strength vector (V m^–1) - E _g electrostatic field strength vector (V m^–1) - F force vector (N) - F Faraday constant (C mol^–1) - H magnetic field strength vector (A m^–1) - i current density (A m^–2) - i _L limiting current density (A m^–2) - i _L ⁰ limiting current density without applied magnetic field (A m^–2) - I current (A) - I _L limiting current (A) - j current density vector (A m^–2) - K reaction equilibrium constant - k reaction velocity constant - k _b Boltzmann constant (J K^–1) - _{m 1}, m ₂ regression parameters (-) - n charge transfer number (-) - q charge on a particle (C) - R gas constant (J mol^–1 K^–1) - T temperature (K) - t time (s) - V electrostatic potential (V) - v particle velocity vector (m s^–1) Greek symbols transfer coefficient (–) - velocity gradient (s^–1) - _MS potential difference between metal phase and point just inside electrolyte phase (OHP) - diffusion layer thickness (m) - ₀ hydrodynamic boundary layer thickness without applied magnetic field (m) - density (kg m^–3) - electrolyte conductivity (^–1 m^–1) - magnetic permeability (V s A^–1 m^–1) - kinematic viscosity (m² s^–1) - vorticity     

Potential distribution and electrode stability in a bipolar electrolysis cell

A computational model is presented, which enables the identification of those zones endangered by corrosion in a bipolar electrolysis cell stack. The method consists of two steps: first the potential profile in the electrolyser is computed by numerical solution of the Laplace equation using the finite difference method; then, making use of the Criss-Cobble correspondence principle, this profile is related to the potential-dependent thermodynamic stabilities of the respective metals. This may be a useful tool in the design of intermittently operating electrolysers (for example those powered by solar energy).Nomenclature A metal phase - A _i single A-phase point - B electrolyte phase - B _i single B-phase point - F Faraday constant - h mesh interval (m) - i local current density (A m^–2) - i ₀ exchange current density (A m^–2) - j local current across the double layer (A) - j _iA,j _iB tangential or normal component of the double layer current (A) - K A, B phase conductivity ratio - m molality mol kg^–1 - R gas constant - T absolute temperature (K) - U potential (V) - U ₀ water decomposition voltage (V) - U _tot end plate potential (V) - x, y cartesian coordinates - overrelaxation factor - _a, _c anodic or cathodic overpotential (V) - _A, _B electrical conductivity (^–1 m^–1) - potential (V) - _m local double layer potential, electrode end (V) - _s local double layer potential, electrolyte end (V)     

Electrode current distribution in a hypochlorite cell

Electrochemical production of gases, e.g. Cl₂, H₂ and O₂, is generally carried out in vertical electrolysers with a narrow electrode gap. The evolution of gas bubbles, on one hand, speeds up the mass transport; on the other it increases the solution resistance and also the cell potential. The gas void fraction in the cell increases with increasing height and, consequently, the current density is expected to decrease with increasing height. Insight into the effects of various parameters on the current distribution and the ohmic resistance in the cell is of the utmost importance in understanding the electrochemical processes at gas-evolving electrodes. An example of the described phenomena is the on-site production of hypochlorite by means of a vertical cell. Experiments were carried out with a working electrode consisting of 20 equal segments and an undivided counter electrode. It has been found that the current distribution over the anode is affected by various electrolysis parameters. The current density,j, decreased linearly with increasing distance,h, from the leading edge of the electode. The absolute value of the slope of theI/h straight line increased with increasing average current density and temperature, and with decreasing velocity of the solution, NaCl concentration and interelectrode gap.Nomenclature a ₁ constant - b _a anodic Tafel slope (V) - b _c cathodic Tafel slope (V) - B current distribution factor - B ₀ current distribution factor att _e=0 - c _NaCl sodium chloride concentration (kmol m^–3) - d_wt interelectrode gap (mm) - h distance from the leading edge of the segmented electrode (m) - H total height of the segmented electrode (m) - I current (A) - I _s current through a segment (A) - j ₀ exchange current density (kA m^–2) - j _av mean current density (kA m^–2) - j _t current density at the top of the segmented electrode (h=H) (kA m^–2) - j _b current density at the bottom of the segmented electrode (h=0) (kA m^–2) - n _s number of a segment of the segmented electrode from its leading edge - R _s unit surface resistance of solution ( m²) - R _{s, b} unit surface resistance of solution at the bottom of the segmented electrode ( m²) - R _{s, t} unit surface resistance of solution at the top of the segmented electrode ( m²) - t _e time of electrolysis (h) - T temperature (K) - U _c cell voltage (V) - U ₀ reversible cell voltage (V) - v ₀ solution flow rate of the bulk solution in the cell at the level of the leading edge of the electrode (m s^–1) - resistivity of the solution ( m) - _a anodic overpotential (V) - _c cathodic overpotential (V) - gas void fraction - _b gas void fraction ath=0 - _t gas void fraction ath=H Paper presented at the 2nd International Symposium on Electrolytic Bubbles organized jointly by the Electrochemical Technology Group of the Society of Chemical Industry and the Electrochemistry Group of the Royal Society of Chemistry and held at Imperial College, London, 31st May and 1st June 1988.     

Electrical measurements in bipolar trickle reactors

Current potential curves for the total current flowing through the reactor and for the current passing through a single ring of the column packing have been measured using solutions containing the ferroferricyanide couple. The theoretical formulation of current-potential plots has been extended to incorporate a fast reversible reaction in the presence of diffusion polarization. A method for deriving the film thickness and mass transfer limiting current from these plots has been provided.List of symbols a integration constant in Equation 6 - b integration constant in Equation 8 - E applied potential (V) - E _r potential of the ring electrode with respect to the feeder electrode at the entry position of the reactor (V) - E ₁,E ₂ reversible potentials of an anodic and cathodic reaction, respectively - F Faraday constant - h film thickness (cm) - I current passing through segmented rings (mA) - I _F Faradaic current per unit length of wetted perimeter (A cm^–1) - I _NF non-Faradaic current per unit length of wetted perimeter (A cm^–1) - I _T total current per unit length of wetted perimeter (A cm^–1) - L half-length of Raschig ring (cm) - i _D limiting mass-transfer controlled current (A cm^–1) - i _D limiting mass transfer controlled current at the end of the rings (A cm^–2) - i_{D, 1mM} limiting mass transfer controlled current for 1 mM of redox couple - i_o1, i_o2 exchange current for two reactions (one anodic and the other cathodic) - n number of electrons transferred in an electrochemical reaction - n ₁,n ₂ number of electrons transferred in two reactions (one anodic and the other cathodic) - n _c number of mmol of ferro-ferricyanide - n _r number of graphite Raschig rings in a single layer of a packed column - r reaction rate (mol cm^–2 s^–1) - R gas constant (8.314JK^–1mol^–1) - r _o,r _i radii of the outer and inner perimeter of the ring (cm) - (Re)_f film Reynolds number (dimensionless) - T temperature (K) - v volumetric liquid flow rate (cm³ min^–1) - x axial co-ordinate along Raschig ring (cm) - ₁, ₂ transfer coefficients for two reactions (one anodic and the other cathodic) (dimensionless) - fraction of the end areas of the rings which overlap (dimensionless) - electrode overpotential (V) - _T total overpotential for half of a bipolar ring (V) - v kinematic viscosity (cm² s^–1) - solution resistivity ( cm) - _s potential in the solution phase (V)     

Mass transfer to and copper deposition on a round bar in a new type of electrolytic cell: the helix cell

High-rate electrodeposition of copper from CuSO₄-H₂SO₄ baths can be achieved by using crossflow of solution. To obtain copper layers of uniform thickness and quality, a new type of electrolytic cell, the helix cell, has been proposed. An experimental dimensionless relation has been given to describe the mass transfer to a round bar, in crossflow, in a helix cell. Moreover, the current efficiency of copper deposition has been obtained as a function of current density, flow rate of solution, temperature and weight per cent CuSO₄ in the CuSO₄-H₂SO₄ solution.Nomenclature A _e working-electrode surface area (m²) - c concentration of Cu²⁺ (mol m^-3) - c _e c at electrode surface (mol m^-3) - c _b c in bulk of solution (mol m^-3) - C constant factor (-) - d _c inner diameter of central cylinder of helix cell (mm) - d _c volumetric hydraulic diameter of helix cell (mm) - d _h width of helical slots in central cylinder of helix cell (mm) - d _s diameter of working electrode (round bar) (mm) - D _i diffusion coefficient of species i (m² s^-1) - F Faraday constant (C mol^-1) - I current (A) - k _i mass-transfer coefficient for a species i (m s^-1) - i current density (kA m^-2, A m^-2) - L _c length of working-electrode compartment of helix cell (m) - n number of electrons involved in electrode reaction (-) - n₁, n₂, n₃ constants (-) - R gas constant: R=8.31 J K^-1 mol^-1 - Re Reynolds number: Re=v _c d _h/v (-) - Sc Schmidt number: Sc=v/D (-) - Sh Sherwood number: Sh=kd _h/D - t time (s) - T temperature (K) - U _s volumetric rate of solution through the helix cell (m³ s^-1) - v _c flow rate of solution through working-electrode compartment of the helix cell (vc = U/(d _c –dw)Lc) (ms–1) - density of solution (kg m ^-3) - u dynamic viscosityofsolution (kg m-1 s-1) - v kinematic viscosity of solution (m2 s-1) - _i current efficiency for formation of a species i (-)     

Experimental investigation of the primary and secondary current distribution in a rotating cylinder Hull cell

A rotating cylinder cell having a nonuniform current distribution similar to the traditional Hull cell is presented. The rotating cylinder Hull (RCH) cell consists of an inner cylinder electrode coaxial with a stationary outer insulating tube. Due to its well-defined, uniform mass-transfer distribution, whose magnitude can be easily varied, this cell can be used to study processes involving current distribution and mass-transfer effects simultaneously. Primary and secondary current distributions along the rotating electrode have been calculated and experimentally verified by depositing copper.List of symbols c distance between the cathode and the insulating tube (cm) - F Faraday's constant (96 484.6 C mol^–1) - h cathode length (cm) - i local current density (A cm^–2) - i _L limiting current density (A cm^–2) - i _ave average current density along the cathode (A cm^–2) - i ₀ exchange current density (A cm^–2) - I total current (A) - M atomic weight of copper (63.54 g mol^–1) - n valence - r _p polarization resistance () - t deposition time (s) - V _c cathode potential (V) - Wa _T Wagner number for a Tafel kinetic approximation - x/h dimensionless distance along the cathode surface - z atomic number Greek symbols _a anodic Tafel constant (V) - _c cathodic Tafel constant (V) - solution potential (V) - overpotential at the cathode surface (V) - density of copper (8.86 g cm^–3) - electrolyte conductivity ( cm^–1) - deposit thickness (cm) - _ave average deposit thickness (cm) - surface normal (cm)     

Design characteristics of an aluminium-air battery with consumable wedge anodes

An attempt was made to optimize a mechanically rechargeable bipolar-cell battery, exemplified by an aluminium-air battery with self-perpetuating wedge anodes. The optimization involved current density of battery operation and some design parameters such as the anode thickness and the cell dimensions. It was shown that these parameters depend on the energy-to-power ratio selected by the user. The saline electrolyte aluminium-air battery was found to be essentially a low power-density/high energy-density power source. Energy densities of up to over 1500 W h kg^–1 are achievable for low power needs, indicating very long operations between recharging. It was also shown that aluminium should render significantly cheaper electric energy than any of the high-energy density metals.Nomenclature d anode plate thickness (cm) - d _p thickness of end-plates (cm) - d thickness of cell walls (cm) (see Fig. 1) - E energy density (W h kg^–1) - E _B total energy contained in the battery (k W h) - F the Faraday constant 26.8 A h mol^–1 - g _c weight of the air cathode per unit anode area (g cm^–2) - g _e excess electrolyte per unit electrode area (g cm^–2) - g _h weight of the hardware per unit anode area (g cm^–2) - g _m weight of metal per unit electrode area (g cm^–2) - _m g excess of unconsumable metal per unit electrode area (g cm^–2) - g ₀ sum of all the weights except that of consumable metal (g cm^–2) - g _ox weight of oxygen consumed withg _m (g cm^–2) - G total weight of battery (g) - G _m total amount of reserve metal per cell and per cm width (kg cm^–1) - G _m total weight of the wedges (kg) - G _r total weight of the reserve anode container except the metal (kg) - G free energy of oxidation of the metal (kW h mol^–1) - h _a height of the wedge (cm) - h _r reserve anode height (cm) - j current density (mA cm^–2) - J total current drawn from the battery (mA) - n number of electrolyte replacements between anode replacement - n _c number of cells in a battery - M atomic weight of the metal (kg mol^–1) - P power density (W kg^–1) - Q _e cost of metal in the cost of unit energy produced ($ kW^–1 h^–1) - Q _e ⁰ theoretical figure of merit of a metal ($ kW^–1 h^–1) - Q _m cost of metal per unit weight ($ kg^–1) - S _a total anode surface area (cm²) - U cell voltage without ohmic drop (V) - V cell voltage (V) - x width of battery (cm) - z number of electrons exchanged per atom of metal dissolved - interelectrode spacing (cm) - spacing between cover and top of a new reserve anode (cm) - _f material efficiency - _v voltage efficiency - _e conductivity of electrolyte (ohm^–1 cm^–1) - _e electrolyte density (g cm^–3) - _m density of metal (g cm^–3) - _p density of end-plates (g cm^–3) - _w density of cell-walls (g cm^–3)     

The behaviour of a trickle tower electrolytic cell for the production of cobalt(III) acetate from cobalt(II) acetate

The production of Co(III) acetate from Co(II) acetate using a bipolar trickle tower of graphite Raschig rings was investigated. Space time yields up to 18 kg m^–3 h^–1 were obtained, which showed no improvement over those achievable in a conventional plate and frame cell. A mathematical model of the system indicated that the electrode reactions occurred almost entirely at the opposing annular surfaces between consecutive layers of Raschig rings and that the unexpectedly low performance of the device was most probably due to the unfavourable mass transport conditions which existed in the intervening gaps.Nomenclature a annular cross sectional area of one Raschig ring (m²) - b _C kinetic exponential constant for reduction of Co(III) (V^–1) - b _A kinetic exponential constant for oxidation of Co(II) (V^–1) - b _H kinetic exponential constant for hydrogen evolution (V^–1) - b ₀ kinetic exponential constant for oxygen evolution (V^–1) - [Co(II)] concentration of Co(II) (mol m^–3) - [Co(III)] concentration of Co(III) (mol m^–3) - F Faraday constant (96 487 C mol^–1) - f fraction of total flow by-passing the annular gap between adjacent Raschig rings in a vertical row - I current per vertical column of rings (A) - k _C rate constant for reduction of Co(III) (A m mol^–1) - k _A rate constant for oxidation of Co(II) (A m mol^–1) - k _H rate constant for hydrogen evolution (A m^–2) - k _O rate constant for oxygen evolution (A m^–2) - k _L mass transfer coefficient (m s^–1) - Q flow rate per vertical row of Raschig rings (m³s^–1) - v volume of annular gap between adjacent Raschig rings in a vertical row (m³) - V superficial velocity of electrolyte (m s^–1) - _A anodic potential (V) - _C cathodic potential (V)     

Modelling of gas-evolving electrolysis cells. III. TheiR drop at gas-evolving electrodes

Based on a potentiostatic interrupter technique theiR drop of the bubble layer in front of gas-evolving electrodes of various shapes has been investigated. At small plane electrodes the dependency ofiR drop on electrode inclination has been studied for hydrogen, oxygen and chlorine evolution. In all systems a slightly up-faced orientation results in a gas bubble layer structure of minimumiR drop. Also for expanded metal electrodes of different shapes theiR drop across the electrode diaphragm gap has been studied. The fractional open cross-section and the inclination angle of the electrode blades have been identified as important parameters with respect to the gas diverting effect. These tendencies have also been confirmed for a pilot cell of 1 m height.Nomenclature b' Tafel slope (V) - c ₀ double layer capacity (F cm^–2) - d thickness (cm) - E electrode potential (V) - F Faraday number (96487 As mol^–1) - i current density (A cm^–2) - R area resistance ( cm²) - R gas constant (8.3144 Ws deg^–1 mol^–1) - T temperature (K) - t time (s) - u _g ⁰ superficial gas velocity (cm s^–1) - u _sw swarm velocity (cm s^–1) - U voltage (V) Greek symbols inclination angle (^o) - symmetry factor (1) - _g gas voidage (1) - _m maximum gas voidage. (1) - overvolgate (V) - electrolyte conductivity (S cm^–1) - _g number of electrons (1) Paper presented at the 2nd International Symposium on Electrolytic Bubbles organized jointly by the Electrochemical Technology Group of the Society of Chemical Industry and the Electrochemistry Group of the Royal Society of Chemistry and held at Imperial College, London, 31st May and 1st June 1988.     

The mechanism of copper powder formation in potentiostatic deposition

A mechanism for copper powder formation in potentiostatic deposition is proposed, and the critical overpotential of copper powder formation is determined. A good agreement between theoretical and experimental results has been obtained.List of symbols C ₀ bulk concentration (mol cm^–3) - D diffusion coefficient (cm² s^–1) - F Faraday's constant (C mol^–1) - h height of protrusion (cm) - h _c height at which dendrites crack (cm) - h _i height (cm) - h ₀ initial height of protrusion (cm) - h _j,t elevation at pointj and timet (cm) - h _j,0 initial elevation at pointj (cm) - I limiting diffusion current (A) - I ₀ initial limiting diffusion current (A) - i limiting current density (A cm^–2) - i _d current density on the tip of dendrite of height h (A cm^–2) - i _t total current (A cm^–2) - j number - k proportionality factor [cm (mol cm^–3)^m] - k constant - M number of dendrites - m number - N number of elevated points - n number of electrons - p concentration exponent - Q _c quantity of electricity (C) - R gas constant (J mol^–1 K^–1) - S electrode surface area (cm²) - T temperature (K) - t time (s) - t _a longest time in which approximation h is valid (s) - t _i induction time (s) - V molar volume (cm³ mol^–1) - surface tension (J cm^–2) - thickness of diffusion layer (cm) - overpotential (V) - _c,p critical overpotential of powder formation (V) - fraction of flat surface - apparent induction time (s)     

Electrochemical reduction of silver thiosulphate complexes Part II Mechanism and kinetics

In this paper the thermodynamic data for complex formation between Ag⁺ and S₂O_{3 2–} ions, determined previously, are applied to kinetic investigation of the reduction of silver thiosulphate complexes. Both electrochemical (linear sweep voltammetry on a rotating disc electrode) and surface analytical (Auger electron spectroscopy) techniques are used. The deposits resulting from the electrodeposition of silver thiosulphate complexes are shown to be composed of silver and to be polycrystalline. The reduction follows a mechanism involving mass and charge transfer and chemical reaction steps. The relevant kinetic parameters are calculated and a rate equation describing the kinetics of the reduction is given.List of symbols a activity (M) - c concentration (M) - j current density (A m^–2) - j _c current density of charge transfer (A m^–2) - j _m current density of mass transfer (A m^–2) - k rate constant (m s^–1) - y activity coefficient (molarity scale) - D diffusion coefficient against gradient of concentration (m² s^–1) - D diffusion coefficient against gradient of electrochemical potential (m² s^–1) - E electrode potential vs NHE (V) - I ionic strength (M) - T temperature (K) Greek symbols a transfer coefficient - _1n stability constant of Ag(S₂O₃) _n (^2n–1)- - kinematic viscosity (m² s^–1) - rotation speed of the electrode (rad s^–1) Indices b bulk of the solution - f free (= uncomplexed) - 1,n related to complex Ag(S₂O₃)_n ^(n–1) - t total Constants F Faraday constant (96486 A s mol^–1) - R universal gas constant (8.3145 Jmol^–1 K^–1)     

An efficient method for solving the model equations of a two dimensional packed bed electrode

A theoretical and experimental study of a flow-by packed bed electrochemical reactor consisting of graphite particles is given. The mathematical model describes the two dimensional distributions of electrode potential and reactant concentration in the reactor, and includes the influence of lateral dispersion between the feeder electrode and membrane. A new efficient numerical method, based on central finite difference and orthogonal collocation is used to solve the model. Results of the model simulations agree well with experimental measurement of the potential distribution for the ferrocyanide/ferricyanide system.List of symbols a specific surface area of packed bed electrode (cm^–1) - c _i concentration of speciesi(i = 2 for cathodic species) (mol dm^–3) - c _i0 inlet concentration of speciesi (mol dm^–3) - C dimensionless concentration - c _s concentration on the electrode surface (mol dm^–3) - C _s dimensionless concentration on the electrode surface - D _s effective diffusion coefficient (cm²s^–1) - Da Damköhler number - F Faraday's constant (96 487 C mol^–1 of electrons) - i current density (A m^–2) - i ₀ exchange current density (A m^–2) - I number of equation - j ₂ electrochemical reaction rate per unit area (mol cm^–2 s^–1) - J number of node point - k _a average local mass transfer coefficient (cm s^–1) - n number of moles of electrons - N number of inner collocation points - N ₂ flux of species 2 (mol cm^–2 s^–1) - Pe Peclet number - R gas constant (8.314 J mol^–1 K^–1) - Sh _m modified Sherwood number - T temperature (K) - u _a average axial velocity (cm s^–1) - x lateral coordinate (cm) - x ₀ electrode depth (cm) - X dimensionless depth of electrode - y axial coordinate (cm) - y ₀ electrode length (cm) - Y dimensionless length of electrode - z ₀ electrode width (cm) Greek symbols aspect ratio - _a anodic transfer coefficient - _c cathodic transfer coefficient - overpotential (V) - stoichiometric coefficient - dimensionless rate constant - ₂ effective conductivity of electrolyte (^–1 cm^–1) - ₁ potential of electrode (V) - ₂ potential of electrolyte (V) - _eq equilibrium potential (V) - dimensionless potential